The Lefschetz fixed point theorem connects the number of rational
points on a separated scheme of finite type over \(\overline{\mathbb {F}}_q\) ,
that is, the number of fixed points of Frobenius, to the trace of
Frobenius acting on étale compactly supported cohomology,
see [1]}.
By work of Behrend [2]}
this result extends to the setting of Deligne-Mumford stacks.
